Let XI , .... Xn be independent random variables. Show
Chapter , Problem 26(choose chapter or problem)
Let XI , .... Xn be independent random variables. Show that Solution. We have ,=1 ' var X, var( TI n X ) n ( ( ) ) TI=1 E[X;] = g E[Xl l + 1 - 1. var(IT X,) = E [IT X;] -IT (E[XiJ)2 ,=1 i=1 i=1 11 n = II E [X;] - II (E[X,J) 2 i= 1 ,=1 n n = II (var(X, ) + (E[X,J) 2) -II (E[XiJ) 2 . 1=1 i=1 The desired result follows by dividing both sides by ,=1
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